Abstract
The present survey is devoted to the investigation of the local times of self-intersection as the most important geometric characteristics of random processes. The trajectories of random processes are, as a rule, very nonsmooth curves. This is why to characterize the geometric shape of the trajectory it is impossible to use the methods of differential geometry. Instead of this, one can consider the local times of self-intersection showing how much time the process stays in “small” vicinities of its points of self-intersection. We try to describe the current state of the theory of local times of self-intersection for Gaussian and related random processes. Different approaches to the definition, investigation, and application of the local times of self-intersection are considered.
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